Electron self-energy effects on chiral symmetry breaking in graphene

We investigate the dynamical breakdown of the chiral symmetry in the theory of Dirac fermions in graphene with long-range Coulomb interaction. We analyze the electron-hole vertex relevant for the dynamical gap generation in the ladder approximation, showing that it blows up at a critical value \alpha_c in the graphene fine structure constant which is quite sensitive to many-body corrections. Under static RPA screening of the interaction potential, we find that taking into account electron self-energy corrections to the vertex increases the critical coupling to \alpha_c \approx 4.9, for a number N = 4 of two-component Dirac fermions. When dynamical screening of the interaction is instead considered, the effect of Fermi velocity renormalization in the electron and hole states leads to the value \alpha_c \approx 1.75 for N = 4, substantially larger than that obtained without electron self-energy corrections (\approx 0.99), but still below the nominal value of the interaction coupling in isolated free-standing graphene.